ISSN 1311-8080 (PRINTED VERSION)

ISSN 1314-3395 (ON-LINE VERSION)

IJPAM: Volume 107, No. 3 (2016)

Abstract. The algebra
arises in number theory and has been studied in [#!BC!#] of Bost and Connes. Laca and Raeburn continued the study in [#!LR!#] and gave an improvement of the theorem of Bost and Connes. This leads us to consider a closely related algebra
because of its interesting connections with -algebras and group algebras.

In this paper we give a detailed proof of Laca and Raeburn's theorem. Then we define a new Hecke pair
and show that the Hecke algebra
is a universal -algebra generated by
the elements
,
and a new element